Manfred Denker
Title: Ergodic averages of multivariate functions

Abstract: Let (X,m,T) be a probability preserving transformation. For a multivariate function h(x₁,...,x_d) I will discuss convergence properties of averages n^-d ∑_{1≤i1,...,id≤n} h(T^i₁(x),..., T^i_d(x)) from the dynamical and ergodic theoretical viewpoints: h may be defined as a function or as an element in some tensor product. In the latter case I will discuss recent results with M. Gordin on the extension of the ergodic theorem, the central limit theorem and the convergence theorem towards generalized χ² distributions.